I'm coining the term here, I think ... not sure what was it called when discussed on Bitcointalk.

Impeccable timing... I just created this wiki page that takes a stab at addressing the very thing you've asked about.

Companies claiming they got hacked and lost your coins sounds like fraud so perfect it could be called fashionable. I never believe them. If I ever experience the misfortune of a real intrusion, I declare I have been honest about the way I have managed the keys in Casascius Coins. I maintain no ability to recover or reproduce the keys, not even under limitless duress or total intrusion. Remember that trusting strangers with your coins without any recourse is, as a matter of principle, not a best practice. Don't keep coins online. Use paper or hardware wallets instead.

It's no harder to generate the initial pair yourself as it is to validate that it is correct. If you don't validate it, and it turns out to be defective in any way, your money is forever lost.

Frankly, this seems silly to me. What advantage do you get from splitting the key in this way?

1 - the ability to put your key in 2 different geographically separate places to protect them from snooping/theft. example, I might put one half in my safety deposit box and keep the other half at home, so someone from the bank who happens to gain access to my safety deposit box doesn't get my bitcoins.

2 - the ability to have 2 separate machines generate a single key, so even if one or both machines is compromised, the resulting key is not. (Example: Smartphone + Computer). All that matters is that both machines aren't compromised by the same person or someone with the ability to access both halves.

Companies claiming they got hacked and lost your coins sounds like fraud so perfect it could be called fashionable. I never believe them. If I ever experience the misfortune of a real intrusion, I declare I have been honest about the way I have managed the keys in Casascius Coins. I maintain no ability to recover or reproduce the keys, not even under limitless duress or total intrusion. Remember that trusting strangers with your coins without any recourse is, as a matter of principle, not a best practice. Don't keep coins online. Use paper or hardware wallets instead.

1 - the ability to put your key in 2 different geographically separate places to protect them from snooping/theft. example, I might put one half in my safety deposit box and keep the other half at home, so someone from the bank who happens to gain access to my safety deposit box doesn't get my bitcoins.

That can be done much simpler ways. For example, you can literally separate the key bits in half. You can also generate a random sequence the same length as the key, and store that along with the key XORed with that.

Quote

2 - the ability to have 2 separate machines generate a single key, so even if one or both machines is compromised, the resulting key is not. (Example: Smartphone + Computer). All that matters is that both machines aren't compromised by the same person or someone with the ability to access both halves.

Any scheme that doesn't involve storing the private key on a single device has this property.

I am an employee of Ripple. Follow me on Twitter @JoelKatz1Joe1Katzci1rFcsr9HH7SLuHVnDy2aihZ BM-NBM3FRExVJSJJamV9ccgyWvQfratUHgN

1 - the ability to put your key in 2 different geographically separate places to protect them from snooping/theft. example, I might put one half in my safety deposit box and keep the other half at home, so someone from the bank who happens to gain access to my safety deposit box doesn't get my bitcoins.

That can be done much simpler ways. For example, you can literally separate the key bits in half. You can also generate a random sequence the same length as the key, and store that along with the key XORed with that.

Agreed, simpler for the computer. (though separating the key bits in half definitely works, is simple for the user, and I've done it).

By writing the proposal, I'm hoping it leads to something simple for the user.

Ultimately, the user should just be able to click a button, and get however many codes he wants. I will probably update my Casascius Bitcoin Utility to generate all of these codes, as well as turn them back into a single standard private key for import.

2 - the ability to have 2 separate machines generate a single key, so even if one or both machines is compromised, the resulting key is not. (Example: Smartphone + Computer). All that matters is that both machines aren't compromised by the same person or someone with the ability to access both halves.

Any scheme that doesn't involve storing the private key on a single device has this property.

No single device can generate a single key without storing it in memory, at least temporarily. And it has to send the key somewhere through some sort of i/o for it to be of any use. Interception is possible at either point by malware that knows what it's looking for. Bottom line, I think most would agree that a wallet generator being immune to an unknown compromise is a desirable feature if it is not too complicated or inconvenient to use.

Using EC multiplication rather than XOR has the convenient property that machine 1 can share what it needs with machine 2 in the form of an EC point (like a public key), and neither machine will ever be able to know the complete final private key until the user redeems the wallet.

Companies claiming they got hacked and lost your coins sounds like fraud so perfect it could be called fashionable. I never believe them. If I ever experience the misfortune of a real intrusion, I declare I have been honest about the way I have managed the keys in Casascius Coins. I maintain no ability to recover or reproduce the keys, not even under limitless duress or total intrusion. Remember that trusting strangers with your coins without any recourse is, as a matter of principle, not a best practice. Don't keep coins online. Use paper or hardware wallets instead.

For the private key splitting, your approach of storing parts combined with a global XOR seems to be redundant against only one failure. But why not expand the concept to an arbitrary (n,k)-redundant encoding? Here's a quick brainstorm of how a scheme might work:

1. Take your private key and find n values (which we'll call v(1) to v(n)) which meet the following conditions:

i. v(k) <= 2 ^ 256 / (k)^(3*n)ii. hex(SHA256(k)) starts with '00' - this is the checksumiii. XOR(v(k) for all k 1 to n) = the original private key

The first condition isn't too important, it's just nice to have if you want all of your pieces to stay within 64 bytes.

Now, for the pieces. Piece k will have the following format (encoded into base 58 of course):

To reconstitute the private key, simply solve the linear system from any three pieces and XOR all the results. You actually don't have to know what n is because you can simply assume that n is the number of pieces that you have, and if you have too many pieces solving the linear system will simply lead you to discover that the n+1st, n+2nd, etc pieces are all equal to zero.

The scheme can easily be adapted to make the private key the EC product of v(1), v(2), etc rather than an XOR, and even the linear systems can be changed to an multiplicative/exponential equivalent if desired, so it's pretty adaptable.

Argumentum ad lunam: the fallacy that because Bitcoin's price is rising really fast the currency must be a speculative bubble and/or Ponzi scheme.

For the private key splitting, your approach of storing parts combined with a global XOR seems to be redundant against only one failure. But why not expand the concept to an arbitrary (n,k)-redundant encoding? Here's a quick brainstorm of how a scheme might work:

If "why not" is a question, the honest answer is because I don't understand the math well enough to propose such a thing, though I agree that an encoding that allows redundancy against an arbitrary number of failures is more desirable than a scheme that allows redundancy against only one, except perhaps if implementing the scheme is too difficult for developers that they just don't do it. (Your suggestion on its surface appears to not have this problem).

If "why not" is a suggestion, well then, hell yeah!

Would you be willing to write your suggestion up on the wiki and assume that your reader doesn't understand the math? For example, when you say "find n values that meet the following conditions", it's not obvious to me how one would go about finding such a value.

Companies claiming they got hacked and lost your coins sounds like fraud so perfect it could be called fashionable. I never believe them. If I ever experience the misfortune of a real intrusion, I declare I have been honest about the way I have managed the keys in Casascius Coins. I maintain no ability to recover or reproduce the keys, not even under limitless duress or total intrusion. Remember that trusting strangers with your coins without any recourse is, as a matter of principle, not a best practice. Don't keep coins online. Use paper or hardware wallets instead.

I'm pretty sure this has already been discussed, but am wondering why it isn't done yet:Here's a spin off the Casascius Coins and Bit Bills. Let's call the website "Rainy Day Savings." Joe creates a key pair and sends the public key to the website and orders a Rainy Day Bill. April at Rainy Day Savings prints a Bill and applies a tamper resistant hologram that conceals a private key. April then generates a 2 of 2 multisig address based on the public key sent to the website and the public key that goes to the hidden private key. That address is printed on the note. April then mails the note to Joe and advises him to carefully write or print the private key paired to the public key that was sent to the website. Joe then sends an amount to the multisig address and writes the value of the note on its face. Joe can then spend the note as physical Bitcoin and because it is multisig signed, nobody has both addresses to spend it until the tamper-proof sticker is removed and both private keys are imported to a wallet.

Any significantly advanced cryptocurrency is indistinguishable from Ponzi Tulips.

Would you be willing to write your suggestion up on the wiki and assume that your reader doesn't understand the math? For example, when you say "find n values that meet the following conditions", it's not obvious to me how one would go about finding such a value.

Would you be willing to write your suggestion up on the wiki and assume that your reader doesn't understand the math? For example, when you say "find n values that meet the following conditions", it's not obvious to me how one would go about finding such a value.

Fairly technical (hard to avoid that when describing these types of protocols), but here you go.

Good news! I got some code working that generates these for any k,n up to 7.

I meant to make it up to 8, but I overflow the amount of space I've given myself when doing an 8 of 8 scheme, so will need to tweak it for that bit to fit. But 7 of 8 won't overflow.

The code totally works!... generating a random key and bitcoin address in n parts, and is able to recreate it with k strings. I modified your proposal a little bit, and then wrote my code to be consistent with it.

Sample! Any 7 of the following 8... (as indicated by prefix 6s7, the 7 means how many is needed):6s755BvvkPDD6VpEZVB8vMbDPDGZSVdEX4BCPGmEdXp1NifbBQ7ALFGnmTN6s75WdT4MPbeYr43nDjFpq944VqRRJJdNKd1Zv9GioScjbt8tUeBjn1fUzN6s75x4yCDj15iukjhH51Td9hJWdXzqVtExFVAVkHwfhHWsqGwUyGhvxyhbG6s76PWVMkSrWktWADeHJDTL743zPbkbXTYNxtWUYbARVVYpTABTr2JwCo886s76px1hvUvTZwfzgF2eZb4BcM2pQCzuKjAvAnsf34T6hvtAhq4BGgmWgtn6s77GPZFG2Twgj1auFPMKYzr4mzckXT4YG5GMZPwqZyjkfqfHGNGnCmuEsf6s77hqEdScKDWpgZM7u158kSE4L4kxYFRDHXrQZQ7R1dautwg7WugaNruau6s789Hp6fCk35xAaKpC9qnFdLD2fZjQx6YQ2RYgX4zTnPxYiexY1yfoHCym

Yields the following bitcoin private key and bitcoin address with my test app. I'm using XOR to combine v(1) thru v(7) once calculated.5KGysrJEuNxE6aZKytbRi9CYTzPefGBrVEG7cWXrnzXq7jte48B13AKe4Ha5XAWWsQWwFqM2EwXiPHjJM2t6v

Any 3 of the following 56s3CKaXLZf36aRuAprra2RmEG94pQdD2hYWyevKzdkVvZ1DWvY9qAVtmPSo6s3Cm23U7kL2Rtod4uTYPUMfLq5akewRNhEbPxhUfWDFiuLtMrnWzFuP3qb6s3DCTZbfzgPzM8FrutYZCwJwjLkrEPfQD1k723bx8Wh1BWLyGBji26PK3G6s3Ddu5jEf2mGR2BxtGzdgbg5Wp2u9XqfJpM7beyNwLuRbu9vwTTB2313sc6s3E5LbrpT2StcHXJuUVRjkKkSqNDUnazAP1qgihyRJNtTEBbVUSz9ajDJS

yields this private key and address.5KELsahJpMfwu7fvMfSMm7rnG5voCTE4P9D6ikR7L6ajeQgpj7U1PWYZB7kLLjm8Ue3pvAEeHMBJr6KXgdR6K

Companies claiming they got hacked and lost your coins sounds like fraud so perfect it could be called fashionable. I never believe them. If I ever experience the misfortune of a real intrusion, I declare I have been honest about the way I have managed the keys in Casascius Coins. I maintain no ability to recover or reproduce the keys, not even under limitless duress or total intrusion. Remember that trusting strangers with your coins without any recourse is, as a matter of principle, not a best practice. Don't keep coins online. Use paper or hardware wallets instead.

Would you be willing to write your suggestion up on the wiki and assume that your reader doesn't understand the math? For example, when you say "find n values that meet the following conditions", it's not obvious to me how one would go about finding such a value.

Math isn't my strong suit. Let me get this straight: m-of-n is when m=n-1K-of-N is when k=n-2

m-of-n and k-of-n are the same... differing only by a letter which was arbitrarily chosen. the only difference is the first proposal I wrote required that m be n-1 (the letters themselves don't matter)... the proposal that Vitalik wrote (which I coded and seems to work) allows m to be as low as 1 and as much as n. If you substitute k for n, everything is the same, you have merely changed the letter.

Companies claiming they got hacked and lost your coins sounds like fraud so perfect it could be called fashionable. I never believe them. If I ever experience the misfortune of a real intrusion, I declare I have been honest about the way I have managed the keys in Casascius Coins. I maintain no ability to recover or reproduce the keys, not even under limitless duress or total intrusion. Remember that trusting strangers with your coins without any recourse is, as a matter of principle, not a best practice. Don't keep coins online. Use paper or hardware wallets instead.

1 - the ability to put your key in 2 different geographically separate places to protect them from snooping/theft. example, I might put one half in my safety deposit box and keep the other half at home, so someone from the bank who happens to gain access to my safety deposit box doesn't get my bitcoins.

That can be done much simpler ways. For example, you can literally separate the key bits in half. You can also generate a random sequence the same length as the key, and store that along with the key XORed with that.

Quote

2 - the ability to have 2 separate machines generate a single key, so even if one or both machines is compromised, the resulting key is not. (Example: Smartphone + Computer). All that matters is that both machines aren't compromised by the same person or someone with the ability to access both halves.

Any scheme that doesn't involve storing the private key on a single device has this property.

With a scheme like this, is it possible to create an interdependence of keys where a community has keys that overlap within and between groups? For instance, an apartment building where everyone needs keys from their next door neighbors with 3 of 5 so either side or two on the same side will do. This would create an interdependent web. If this works, it would make for some interesting banking schemes.

Any significantly advanced cryptocurrency is indistinguishable from Ponzi Tulips.

This won't yet print any M-of-N paper wallets - it will simply produce the M-of-N codes (which you can copy and paste away), and recombine any M of them back into a regular private key (if you copy and paste them back in). It could probably use a lot of scrutiny and testing, but it seems to work like it should.

Companies claiming they got hacked and lost your coins sounds like fraud so perfect it could be called fashionable. I never believe them. If I ever experience the misfortune of a real intrusion, I declare I have been honest about the way I have managed the keys in Casascius Coins. I maintain no ability to recover or reproduce the keys, not even under limitless duress or total intrusion. Remember that trusting strangers with your coins without any recourse is, as a matter of principle, not a best practice. Don't keep coins online. Use paper or hardware wallets instead.